A127355 Primes with prime digit counts. The digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.

3, 7, 17, 23, 71, 101, 103, 107, 109, 113, 127, 131, 137, 173, 199, 223, 233, 271, 311, 313, 317, 331, 359, 367, 409, 479, 499, 593, 673, 677, 701, 709, 773, 797, 907, 919, 929, 947, 953, 977, 991, 1009, 1123, 1129, 1193, 1213, 1217, 1223, 1231, 1277, 1291

Offset: 1

Author

Lekraj Beedassy, Jan 11 2007

Keywords

• nonn
• base

Comments

Compare with "Look And Say" version A056815.

Examples

			The primes 479,991,1747 respectively have digit counts 141719 (one 4,one 7,one 9), 1129 (one 1, two 9's), 111427 (one 1, one 4, two 7's) which are also prime; So they belong to the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A047842, A127354.

Programs

Haskell

a127355 n = a127355_list !! (n-1)
a127355_list = filter ((== 1) . a010051' . a047842) a000040_list
-- Reinhard Zumkeller, Apr 14 2014

Mathematica

dc[n_] :=FromDigits@Flatten@Select[Table[{DigitCount[n, 10, k], k}, {k, 0, 9}], #[[1]] > 0 &];Select[Prime@Range[210], PrimeQ[dc[ # ]] &] (* Ray Chandler, Jan 16 2007 *)

Formula

A010051(a(n)) * A010051(A047842(a(n))) = 1. - Reinhard Zumkeller, Apr 14 2014

Extensions

Corrected by Ray Chandler, Jan 16 2007